Why shrinkwrap not working on the mesh
Are you shrink-wrapping to a single object? You're only allowed a single target object in the shrink-wrap modifier. You can duplicate and merge your objects for the shrink-wrap process; that way, your original model state stays intact.

Also, if you are using other modifiers, play with the order of your modifiers by using the up and down arrow buttons in the modifier panel. I believe modifiers occur from the top down.

Lastly, the shrink-wrap modifier can only work with the geometry its given. subdividing your sheets will add more geometry and give you a more accurate wrap.

Hope this helps!

EDIT:
After downloading your file and applying the methods I described above in a few clicks, I achieved the result you were searching for. There was not enough geometry in the 'sheets'. Also take note of the offset value in the shrink-wrap modifier. see image below: